The Poincaré Recurrence Theorem

  • John C. Oxtoby
Part of the Graduate Texts in Mathematics book series (GTM, volume 2)


In the course of his studies in celestial mechanics, Poincaré discovered a theorem which is remarkable both for its simplicity and for its far-reaching consequences. It is noteworthy also for having initiated the modern study of measure-preserving transformations, known as ergodic theory. From our point of view, this “recurrence theorem” has a special interest, because in proving it Poincaré anticipated the notions of both measure and category. Publication of his treatise, “Les méthodes nouvelles de la mécanique céleste” [29], antedated slightly the introduction of either notion.


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Copyright information

© Springer-Verlag New York Inc. 1980

Authors and Affiliations

  • John C. Oxtoby
    • 1
  1. 1.Department of MathematicsBryn Mawr CollegeBryn MawrUSA

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